With the perturbatively calculated \(F_0^{(1)}\)  and \(F_0^{(2)}\) , in terms of a finite but vanishing photon mass, one can apply and test for Coulomb scattering the method advocated in Ref. [1]} for unitarizing graviton-graviton scattering. In terms of those perturbative PWAs the unitarized formula for \(T_0(p)\)  reads


T0(p)=F0(1)(p)2F0(1)(p)-F0(2)(p) ,

as an application of the Inverse Amplitude Method [2]}, [3]}, [4]}, [5]}. However, when taking \(\mu \rightarrow 0\)  the previous formula collapses to


0T0(p)=i2mp ,

without any dynamical content, in contradiction with the (black) solid line in Fig. REF  or with the existence of the ground state of the Hydrogen atom. Therefore, the method of Ref. [1]} fails to reproduce Coulomb scattering and, in general, is not suitable to unitarize infinite range interactions.
